2007/03/24 by Michael Ben-Or, M. Ben-Or, Avinatan Hassidim +2 · 1 citation
Computer Science · Physics and Astronomy · #Algorithms and Data Compression #FOS: Physical sciences #Machine Learning and Algorithms #Optimization and Search Problems #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0703231
10 pages no figures
openalex publication_date 2007/03/24 · arxiv created 2007/11/09 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability 1 - p. 2. At each stage k comparisons can be performed in parallel and a noisy answer is returned We present a (classic) algorithm which optimally solves both variants together, up to an additive term of O(log log(n)), and prove matching information theoretic lower bounds. We use the algorithm to improve the results of Farhi et al \citeFGGS99 presenting a quantum (error free) search algorithm in an ordered list of expected complexity less than (log2n) / 3.